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On Popa’s factorial commutant embedding problem
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-08-06 , DOI: 10.1090/proc/15141 Isaac Goldbring
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-08-06 , DOI: 10.1090/proc/15141 Isaac Goldbring
Abstract:An open question of Sorin Popa asks whether or not every 
-embeddable factor admits an embedding into 
with factorial relative commutant. We show that there is a locally universal McDuff II
factor 
such that every property (T) factor admits an embedding into 
with factorial relative commutant. We also discuss how our strategy could be used to settle Popa's question for property (T) factors if a certain open question in the model theory of operator algebras has a positive solution.
中文翻译：
关于Popa的阶乘可交换嵌入问题
摘要：索林·波帕（Sorin Popa）的一个悬而未决的问题是，每个可嵌入因子是否都允许以阶乘相对交换形式嵌入。我们表明，存在一个局部通用的McDuff II因子，使得每个属性（T）因子都允许嵌入有阶乘相对可交换的。我们还讨论了如果算子代数模型理论中的某个开放性问题具有肯定的解决方案，那么如何使用我们的策略来解决Popa的属性（T）因素问题。
更新日期：2020-09-02
-embeddable factor admits an embedding into with factorial relative commutant. We show that there is a locally universal McDuff II factor such that every property (T) factor admits an embedding into with factorial relative commutant. We also discuss how our strategy could be used to settle Popa's question for property (T) factors if a certain open question in the model theory of operator algebras has a positive solution. 中文翻译：
关于Popa的阶乘可交换嵌入问题
摘要：索林·波帕（Sorin Popa）的一个悬而未决的问题是，每个可嵌入因子是否都允许以阶乘相对交换形式嵌入。我们表明，存在一个局部通用的McDuff II因子，使得每个属性（T）因子都允许嵌入有阶乘相对可交换的。我们还讨论了如果算子代数模型理论中的某个开放性问题具有肯定的解决方案，那么如何使用我们的策略来解决Popa的属性（T）因素问题。
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